7th grade unit rates

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Vocabulary Review Unit Rates
• A ratio is a comparison of two quantities by division.
̶
17 out of 20 students, or 17
20
• A rate is a special type of ratio comparing two
quantities with different units.
– Driving 120 miles in 2 hours, or
120 miles
2 hours
• A unit rate is a rate that is simplified so that it has a
denominator of 1 unit.
– Driving 120 miles in 2 hours, or 120 miles  60 miles
2 hours
1 hour
Ratios
• A ratio is a comparison of two numbers.
o Example: Tamara has 2 dogs and 8 fish.
The ratio of dogs to fish can be written in
three different ways.
Rate
• What is a rate?
– A rate is a ratio with 2 different units(measurement)
• What is an example of a unit?
– You ran 5 miles in 2 hours. A rate to represent you
running would be 5 miles
2 hours
– 5 apples cost $2.00. A rate to represent the cost of
the apples would be $2.00
5 apples
Unit Rate
• What is a unit rate?
– A unit rate is a rate with a denominator of 1.
• Do unit rates of two different units?
– YES, unit rates are rates and rates have two different
units!
• How do we find unit rate?
– 1st: Set up a unit rate
– 2nd: Divide by the denominator
– 3rd: Write your answer in word form (the numerator
PER the denominator).
Example 1:
Andy biked 24 miles in 4 hours. If he
traveled at a constant speed, how many miles
did he ride in 1 hour?
Write a verbal model of
what you are comparing.
Substitute in the values
given for each quantity.
Since a unit rate has a
denominator of 1 unit,
divide the numerator and
denominator by 4.
miles
hours
24 miles
4 hours
24  4
44

6 miles
1 hour
Andy biked 6 miles per hour.
Example 2:
A 12-pack of Gatorade costs $13.44.
What is the unit price per bottle?
Write a verbal model of
what you are comparing.
Substitute in the values
given for each quantity.
Divide the numerator and
denominator by 12 to find
the unit rate.
cost
bottle
$13.44
12 bottles
$ 13 . 44  12
12  12

$1.12
1 bottle
The unit price is $1.12 per bottle.
Brianna posted a picture of her puppy on Instagram. When she checked her
Phone 4 hours later she had 152 likes. How many likes did she get for her
Picture per hour ?
Blake posted a picure of his adorable kitten at the same time Brianna
posted her picture of her puppy. 6 hours later he checked his phone and he
had 228 likes. How many likes did he get for his adorable kitten?
Who has more likes per hour?
Are the rates the same? Explain.
Example 3:
The price of three different bags of
cat food are shown in the table to the right.
Which bag has the lowest price per pound?
Write a verbal model of
what you are comparing.
For the 3.5 lb bag,
price
$4.83  3.5
$9.45  7
77
For the 20 lb bag,
3.5
4.83
7
9.45
20
27.20
pound
3.5  3.5
For the 7 lb bag,
Cat Food Prices
Size of bag
Price
(lbs)
($)

1 lb

$27.20  20
20  20
$1.38
$1.35
1 lb

$1.36
1 lb
The 7 pound bag is the least expensive at $1.35 per pound
Example 4:
After 3.5 hours, Peyton had traveled 161miles. If she travels at
a constant speed, how far will she have traveled in 4 hours?
Write a verbal model of
what you are comparing.
Find the unit rate in
miles per hour.
miles
hours
161 miles  3.5
3.5 hours  3.5
Multiply the unit rate, or average speed,
by the number of hours traveled.

46 miles
1 hour
46 miles
( 4 hours)  184 miles
1 hour
Peyton travels 184 miles in 4 hours.
Complex fraction
• Complex fractions are fractions that have
fractions within them. They are either in the
numerator, denominator, or both.
• Divide complex fractions by multiplying
Example 5:
Jerry can jog 1⅓ miles in ¼ hour. Find
his average speed in miles per hour.
Write a verbal model of
what you are comparing.
Substitute in the values
given for each quantity.
miles
hour
1
1
3
1
miles
hour
4
Since average speed in
miles per 1 hour, divide
the numerator and
denominator by ¼ .
44 
1
  miles
1 
5 miles
3 4  3 1 
 3
1 1
1 hour
1 hour

4 4
1
1
Jerry jogs at an average speed of 5 ⅓ miles per hour.
Example 6:
Mr. Isaacs is spreading mulch in his yard.
He spreads 4⅔ square yards in 2 hours. How
many square yards can he mulch in 1 hour?
Write a verbal model of
what you are comparing.
sq. yds.
Substitute in the values
given for each quantity.
2
Divide the numerator and
denominator by 2 to find
the unit rate.
hours
4
miles
3
2 hours
14  1 
1
  sq. yds.
4 
2 sq.yds.
3 1  3 2 
 3
22
1 hour
1 hour
2
2
Mr. Isaacs can mulch 2 ⅓ square yards per hour.

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